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CHAOTIC HOMEOMORPHISMS OF Rn, LIFTED FROM TORUS HOMEOMORPHISMS

Published online by Cambridge University Press:  01 September 1999

STEVE ALPERN  and
V. S. PRASAD
STEVE ALPERN
Affiliation:
London School of Economics and Political Science, Houghton Street, London WC2A 2AE
V. S. PRASAD
Affiliation:
Department of Mathematics, University of Massachusetts, Lowell, MA 01854, USA
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Abstract

We establish the existence of self-homeomorphisms of Rn, n [ges ] 2, which are chaotic in the sense of Devaney, preserve volume and are spatially periodic. Moreover, we show that in the space of volume-preserving homeomorphisms of the n-torus with mean rotation zero, those with chaotic lifts to Rn are dense, with respect to the uniform topology. An application is given for fixed points of 2-dimensional torus homeomorphisms (Conley–Zehnder–Franks Theorem).

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 5 , September 1999 , pp. 577 - 580
Copyright
© The London Mathematical Society 1999

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